Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.PrintWriter;
import java.util.*;

public class First {
    public static void main(String[] args) throws IOException {
        Scanner scan = new Scanner(System.in);
        PrintWriter writer  = new PrintWriter(System.out);
        int n = scan.nextInt();
        if (n % 2 == 0) {
            int middle = (n / 2) + 1;
            writer.println(middle);
            int x = 1 + 0;
            int y = 1 + 0;
            for (int i = 1-1; i < n; i++) {
                writer.println(x + " " + y);
                if (i % 2 == 0) {
                    y++;
                }
                else {
                    x++;
                }
            }
        }
        else {
            int m = ((n + 1) / 2);
            writer.println(m);
            int first = 1 + 0;
            int second = 1 + 0;
            for (int i = 1-1; i < n; i++) {
                writer.println(first + " " + second);
                if (i % 2 == 0) {
                    second++;
                }
                else{
                    first++;
                }
            }
        }
        writer.close();
    }
}